The Golden Circle and the Aureate Circle

Abstract

AbstractWe define golden triples to be triples of integers satisfying a particular quadratic equation. The first two elements of each triple are consecutive terms of a Fibonacci-like sequence. We show that each golden triple can be represented by a rational point on a particular circle, which we call the golden circle. We also generate a related circle called the aureate circle. AcknowledgmentSupport for this project was provided by a PSC-CUNY Award, jointly funded by the Professional Staff Congress and the City University of New York.Additional informationFundingSupport for this project was provided by a PSC-CUNY Award, jointly funded by the Professional Staff Congress and the City University of New York.Notes on contributorsHoward SpornHoward Sporn (hsporn@qcc.cuny.edu) is an associate professor of mathematics at Queensborough Community College in Bayside, NY. He received his Ed.D. in mathematics education from Teachers College, Columbia University. Previously, Sporn earned M.S. degrees in mathematics and physics from Stony Brook University. His research interest is number theory. He also likes philosophy, history, movies, science fiction, and cats. He lives on Long Island, NY, with his wife Sharon.